There are 1 questions in this calculation: for each question, the 2 derivative of y is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{2x}{sqrt({x}^{2} + {y}^{2})}\ with\ respect\ to\ y：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2x}{sqrt(x^{2} + y^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2x}{sqrt(x^{2} + y^{2})}\right)}{dy}\\=&\frac{2x*-(0 + 2y)*\frac{1}{2}}{(x^{2} + y^{2})(x^{2} + y^{2})^{\frac{1}{2}}}\\=&\frac{-2xy}{(x^{2} + y^{2})^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2xy}{(x^{2} + y^{2})^{\frac{3}{2}}}\right)}{dy}\\=&-2(\frac{\frac{-3}{2}(0 + 2y)}{(x^{2} + y^{2})^{\frac{5}{2}}})xy - \frac{2x}{(x^{2} + y^{2})^{\frac{3}{2}}}\\=&\frac{6xy^{2}}{(x^{2} + y^{2})^{\frac{5}{2}}} - \frac{2x}{(x^{2} + y^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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